Question

Do this ASAP!! Pardon

Answer 1

Hey mate ♥ here is ur answer

Answer 2

Answer:

9x² - 28x + 3

Step-by-step explanation:

Given Quadratic Equation is 3x² - 4x + 1.

Given that α,β are zeroes of the quadratic polynomial.

(i) Sum of roots:

α + β = -b/a

α + β = 4/3

(ii) Product of roots:

αβ = c/a

αβ = 1/3

We now desire quadratic polynomial whose zeroes are α²/β and β²/α.

(i) Sum of roots:

α²/β + β²/α

= (α³ + β³)/αβ

= [(α + β)³ - 3αβ(α + β)]/αβ

= [(4/3)³ - 3 * 1/3(4/3)]/1/3

= [64/27 - 4/3]/1/3

= 28/9

(ii) Product of roots:

⇒ α²/β * β²/α

⇒ αβ

⇒ 1/3

Hence, the required quadratic polynomial = x² - (28/9) x + 1/3

⇒ 9x² - 28x + 3.

Hope it helps!